Abstract: Systems and methods for determining a probability of changing from one state to another in a stochastic entity, comprising: determining the compact component matrix utilizing characteristic information of the stochastic entity; determining the compact composite component matrix by taking a Kroneker product of the compact component matrix and an identity matrix; determining and placing all current states for the stochastic entity into a state space matrix; determining a Q matrix and/or a transition rate matrix using the compact composite component matrix and basic conditions or variables of the problem domain and/or a compact transition rate matrix; and performing Markov chain Monte Carlo (MCMC) simulation using information from the state space matrix and information from the transition rate matrix to determine the probability of changing from one state to another state in the stochastic entity.